numbers_strings([], []).
numbers_strings([A|As], [B|Bs]) :-
    number_string(A, B),
    numbers_strings(As, Bs).

read_file(Stream, X) :-
    \+ at_end_of_stream(Stream),
    read_line_to_codes(Stream, C),
    string_chars(S, C),
    split_string(S, ",", "", Y),
    numbers_strings(X, Y),
    at_end_of_stream(Stream).

main :-
    open('../input/07', read, Stream),
    read_file(Stream, Lines), !,
    close(Stream),
    msort(Lines, L),
    min_list(L, A),
    max_list(L, B),
    bin_search(A, B, L, N),
    print(N).

tri(A, B) :-
    B is (A * (A + 1)) // 2.

calculate_diff([], _, 0).
calculate_diff([A|As], X, B) :-
    calculate_diff(As, X, B0),
    tri(abs(A - X), T),
    B is B0 + T.

bin_search(L, L, A, Ans) :-
    calculate_diff(A, L, Ans). 
bin_search(L, R, A, Ans) :-
    L < R,
    M is (L + R) // 2,
    ((M >= R, A1 is 9999999999999999); bin_search(L, M, A, A1)),
    ((M =< L, A2 is 9999999999999999); bin_search(M, R, A, A2)),
    Ans is min(A1, A2).